Gibbs Sampling in Factorized Continuous-Time Markov Processes
This enables scalable inference for multi-component continuous-time processes, which is incremental but addresses a known bottleneck in applications requiring reasoning over time.
The authors tackled the problem of exact inference in Continuous-Time Bayesian Networks being computationally infeasible for multi-component processes, and developed a novel Gibbs sampling procedure that provides asymptotically unbiased approximation while reducing computational cost by exploiting network structure.
A central task in many applications is reasoning about processes that change over continuous time. Continuous-Time Bayesian Networks is a general compact representation language for multi-component continuous-time processes. However, exact inference in such processes is exponential in the number of components, and thus infeasible for most models of interest. Here we develop a novel Gibbs sampling procedure for multi-component processes. This procedure iteratively samples a trajectory for one of the components given the remaining ones. We show how to perform exact sampling that adapts to the natural time scale of the sampled process. Moreover, we show that this sampling procedure naturally exploits the structure of the network to reduce the computational cost of each step. This procedure is the first that can provide asymptotically unbiased approximation in such processes.